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Sharygin Geometry Olympiad
2017 Sharygin Geometry Olympiad
3
Power×area
Power×area
Source: Sharygin final round 2017
July 31, 2017
geometry
Problem Statement
A
B
C
D
ABCD
A
BC
D
is convex quadrilateral. If
W
a
W_a
W
a
is product of power of
A
A
A
about circle
B
C
D
BCD
BC
D
and area of triangle
B
C
D
BCD
BC
D
. And define
W
b
,
W
c
,
W
d
W_b,W_c,W_d
W
b
,
W
c
,
W
d
similarly.prove
W
a
+
W
b
+
W
c
+
W
d
=
0
W_a+W_b+W_c+W_d=0
W
a
+
W
b
+
W
c
+
W
d
=
0
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